**265 trigonometry questions.**

I tried to build a isosceles triangle in the middle of a 100 x 100 matrix with two For-loops. The first one is for the horizontal points and the second one for the vertical ones.
At the end of my ...

My code returns this result involves trigonometric functions,
...

It can be verified that the trigonometric expression
$\displaystyle \frac{2 \sin (x)+\sin (2 x)}{(\cos (x)-1) \sqrt{\cos ^3(x)+\cos ^2(x)+\cos (x)}}$
is equal to
$\displaystyle -\frac{2 \sin (x) (\...

I’d like to use the TrigReduce function on a sum of n sinusoids to any power, and am running into an issue with Mathematica’s default ordering of symbols. Is there a way that I can specify an order ...

I have this expression2 Csc[2 y[x2]] Sech[x[x2]]^2 (Cos[y[x2]]^4 Cosh[x[x2]]^8 Sin[y[x2]]^4)^(1/4)which is 1. But Mathematica doesn't do the simplification. I ...

I manipulate equations which are trigonometric equations in mechanics. In theses equations, the custom is to use only Cos, Sin and Tan functions and not the secant and cosecant functions.
To prevent ...

I am trying to figure out how to do the following exercise in Mathematica
Graph $y(t)= a \cos t + b \sin t - 0.5 \sin t$ on the interval $0 ≤ t ≤ 6\, π$

I am given a solution $v_1$(t)=$-e^{t/2}cost$ for a system of first order ODE and I am asked to verify this solution can solves the linear second order ODE in terms of $y_1$(t)
Here is the matrix ...

I want to define a function as suchg[n_] := Assuming[1<=x<=2, NSolve[n==-2 Cos[Pi x], x]]However the result comes out as a conditional expression, for ...

I want to generate (and eventually sample) a sine wave with a random frequency in the range [½, 1] (i.e. capture somewhere between half and one period of the waveform over the domain [0,1]).
The two ...

I am trying to integrate an equation that requires an angle term calculated using ArcTan[x,y]. A number of issues have been mentioned about ...

How can the following trigonometric system of equations be solved numerically?
...

I am new to this and I've plotted this:Plot[3 ArcSin[x + 4] - 16, but I don't know what/how to specify the range?

I want to solve the trigonometric equation :
$$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$
I triedSolve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x]It returns the ...

I'm trying to determine the angle x in the triangle shown below.
Given $\overline{DB}=\overline{DE}$
Given $\overline{AD}=\overline{DC}$
Given $\angle ADE=40^°$
Find $\angle DCB$
But I'm finding ...

I have a bunch of data to which I've assigned units using Quantity, including some angular measurements in degrees. I'd like to be able to use these measurements ...

To solve this problem just follow this rule or is there another possibility?Solve[(3 Sqrt[2])/Sin[60 Degree] == x/Sin[45 Degree], {x}]

I am new to SE Mathematica, and search gives no answer; so here is my problem:
During the testing of my numerical library for quaternions with Mathematica (package Quaternions) I observed the ...

I am trying to solve an equation in Wolfram Mathematica and I get different results although the equation is technically the same. I am really confused. so basically:
$\sin(2x) - \cos(2x)= 1$ is the ...

I am wondering why this simplification does not work,FullSimplify[Im[1/Sin[a]], Assumptions -> Element[a, Reals]]
(*Out[1]= Im(csc(a))*)while this does:<...

I have the following differential equation
...

This question must be too simple, but it confused me for several days. I want to know how can I do the following simplification using Mathematica:
For example, convert ...

Update
This bug has been fixed in v11.3.0.
And as @Carl Woll has pointed out, the imaginary part of Sin and negative sign of Cos...

I have a complex expression with real positive variables only.
Mathematica Input Style:
...

I have a coordinate system generated by :coord = Table[{x, y}, {x, 5}, {y, 5}]I would like to calculate ArcTan(y/x) and ...

There are at least a few non-overlapping triangles made by the lines in the following graphic, how would I isolate them?
...

This seems really easy and I'm probably just messing up on the syntax somewhere (I'm pretty new to Mathematica and I did pour through the Solve page trying to find an answer). I'm basically ...

Good morning,
I want to find a solution to the following equation:
$$\left|u\cdot\sin\left(2\pi\cdot f\cdot t\right)\right|=u\cdot\exp\left(-\frac{t}{a}\right)\space\Longleftrightarrow\space t=\dots\...

Is there any mechanism in Mathematica to simplify ArcTan[Tan[t]] to t? The functions Simplify...

can somebody help me with understanding this equation?
q=1/sqrt(1-j*tan(x))
if tan(x)<<1, then q=1+0.5*j*tan(x)
why?

I'm new to using Mathematica, and I have a problem with plotting Fourier series partial sums.
In particular, my target is
to plot the Fourier series of my piecewise function and with that function ...

When I try to evaluate the limit
$$\lim_{x\to\infty}x\sin(2\pi e x!)$$
Mathematica yields Indeterminate as an answer, however, the solution is known to be $2\pi$. What could be the cause of this ...

I am trying to understand how WolframAlpha reduces the following trig expression
$$ \frac{\ln \left(\sin \left(\frac{\alpha x}{2}\right)+\cos \left(\frac{\alpha
x}{2}\right)\right)}{\alpha }-\...

Suppose I have a list of values of a function $f(x)$ at positive integer points, say
$$f(1) = -0.5, f(2) = -0.5, f(3) = 1, f(4) = -0.5, f(5) = -0.5, f(4) = 1,...$$
Can I interpolate a cosine function, ...

After some calculations, Mathematica gives me a result which has in it a term Cos[2.x] (I cannot skip numerical computing, that's the reason for the ...

I was able to obtain some indefinite integrals for the trigonometric function manually,
$\Gamma^{pq}_n = \int \frac {\cos^p x \sin^q x} {(1+A \cos x)^n} dx$
for $(p,q,n)\geq 0$ in recursive form. ...

How to find indefinite integrals for the rational trigonometric functions of the form
$\qquad\Lambda^{pq}_m = \int \frac{\cos^p x\sin^q x}{(a+b\sin x +c\cos x)^m} dx$
where $(p,q,m)>0$ using ...

Consider the Root objectsroots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}]These can be expressed in terms trigonometric functions as ...

In many cases involved compute the aera or volume, Mathematica always gives the result contains sum of inverse trigonometric functions. In fact, the result can be simplified contains only one inverse ...

I wonder how to implement certain simplifications that one can "see" but Mathematica's Simplify or similar functions aren't finding...
The particular MWE I have here is:
...

Mathematica provides the following function to compute the arctangent of a number, preserving quadrant information:ArcTan[x,y]for real $x$ and $y$, when $y = 0$...

I have a long expression which is not fully simplified because Abs[Sin[4a]] is considered different from 2 Sin[2 a] Abs[Cos[2 a]]...

Ok, I need some great help otherwise I'll go nuts.
I have this function:
$$f(s) = \frac{\pi}{2\sqrt{s}} - \frac{\text{arcsec}(\sqrt{s})}{\sqrt{s-1}}$$
What I have to do is to take $s = +i\omega$, ...

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